NEW YORK — All the momentum the Tampa Bay Rays brought with them to Yankee Stadium on Monday after their big weekend in Baltimore could have sailed into the Bronx night along with the game-changing home run by Brian Roberts in the bottom of the ninth inning.

But all that home run did, aside from ending Chris Archer’s chance at placing his name alongside a legendary pitcher and ruining Joel Peralta’s chance at a save, was make for a longer night and a sweeter victory.

The Rays shrugged off Roberts’ homer and outlasted the New York Yankees, winning in 12 innings after Logan Forsythe singled home Brandon Guyer for a 4-3 victory.

“It was a strange game,” Rays manager Joe Maddon said. “A great game, then a strange game, then it becomes wonderful because you win it.”

And you know how Maddon feels about extra-inning victories that come on the road.

It builds moral, and for this Rays team that has finally found their footing after an awful start the season, it builds more confidence.

“Anytime you come back, especially when you’re winning a ball game and they tie it up, that’s huge,” Forsythe said. “That gives everybody in the clubhouse some confidence. Everybody believes I can be that guy. I think that was a big win all around.”

The Rays, now 4-1 on this 11-game road trip, have won 12 of their last 19 games. They are also 9 ˝ games behind the first-place Blue Jays in the American League East, the first time they’ve been less than 10 games out of first since May 31.

“We’re starting to play really good baseball right now,” Forsythe said.

Archer allowed two runs in seven innings and was in line for the victory had Peralta been able to nail down the save. That would have given Archer five wins in his first five games against the Yankees, something only Hall of Famer Walter Johnson accomplished.

Instead, the win went to Brad Boxberger, who pitched the final two innings and helped the Rays set the major league record for strikeouts in a month when he got Ichiro Suzuki swinging to start the bottom of the 12th.

That was strikeout No. 287 during the month of June for the Rays’ pitching staff, which is one more than the Chicago Cubs recorded during August 2002.

“It’s pretty fun to say I was a part of it,” Boxberger said.

Solo home runs by Matt Joyce in the first inning and Kevin Kiermaier in the third inning gave the Rays a 2-0 lead.

Joyce’s home run was his third in six at-bats after he homered twice Sunday as part of his five-hit day in Baltimore.

Keirmaier’s home run, which came during his first-ever at-bat at Yankee Stadium, gave him three in three games. He and Evan Longoria are the only rookies in team history to accomplish that feat.

But the Yankees tied the score with two runs in the bottom of the third inning.

The rally began when Archer hit Suzuki with a two-strike pitch. Brett Gardner then grounded a ball just inside first base and into the right-field corner. The ball skipped past Kiermaier, allowing Suzuki to race around the bases.

Derek Jeter grounded out to second, and Gardner was able to score the tying run.

“Ground ball down the line, ground ball to second and all of a sudden it’s 2-2,” Maddon said.

The Rays went ahead in the top of the eighth inning when Ryan Hanigan singled with two outs to score Guyer from second base. Guyer began the two-out rally when he drew a walk. A walk to Forsythe moved Guyer into scoring position.

Rays reliever Jake McGee survived an eventful eighth inning that included a soft single to right field by Jacoby Ellsbury and a fly ball to shallow left field that Guyer dropped while trying to make a diving catch.

But McGee pitched out of the jam when he got Carlos Beltran to foul out to Hanigan.

Peralta, trying for only his second save this season as part of Maddon’s closer-by-committee, allowed his seventh home run of the year.

Maddon said Peralta threw the right pitch – a fastball. He just threw it in the wrong location to the switch-hitting Roberts, who was batting left-handed.

“He threw it down to his swing path, and he hit it,” Maddon said.

Peralta got out of the inning, and former closer Grant Balfour got the Rays through to the 10th.

The Rays left the bases loaded in the 11th when Ben Zobrist and Joyce struck out.

In the 12th inning, Guyer drew another two-out walk, stole second and easily scored on Forsythe’s hit.

Boxberger sent the Yankees down in order for a second inning to close out the night.

“To win on the road in extra innings is really is good for a team’s moral, and it really builds,” Maddon said. “Now, I would have liked for Joel Peralta to have gotten three outs and he comes in here feeling like King Kong, and that’s good for him and us. But to lose a game like this would have been really hard to walk in here, very difficult. You don’t know what kind of negative impact it would have.”

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